Question: Simplify the expression. $(-q^{4}-5q^{3})(q^{4}+2q^{3}-7q^{2})$
Explanation: First use the distributive property. $ - q^4 ( q^4) - q^4 (2 q^3) - q^4 (-7 q^2) - 5 q^3 ( q^4) - 5 q^3 (2 q^3) - 5 q^3 (-7 q^2) $ Simplify. $ - 1q^{8} - 2q^{7} + 7q^{6} - 5q^{7} - 10q^{6} + 35q^{5} $ $-q^{8}-7q^{7}-3q^{6}+35q^{5}$ Identify like terms. $ {- 1q^{8}} \color{#DF0030} {- 2q^{7}} {+ 7q^{6}} \color{#DF0030} {- 5q^{7}} {- 10q^{6}} {+ 35q^{5}} $ Add the coefficients. $ { -q^{8}} \color{#DF0030} { -7q^{7}} { -3q^{6}} {+ 35q^{5}} $